What's inaSemantic Network?
James 17. A lien
Alan M. Frisch
Computer Science Department
The University of Rochester
Rochester, NY 14627
Abstract
Ever since Woods's "What's ina Link" paper, there
has been a growing concern for formalization in the
study of knowledge representation. Several arguments
have been made that frame representation languages and
semantic-network languages are syntactic variants of the
ftrst-order predicate calculus (FOPC). The typical
argument proceeds by showing how any given frame or
network representation can be mapped to a logically
isomorphic FOPC representation. For the past two years
we have been studying the formalization of knowledge
retrievers as well as the representation languages that
they operate on. This paper presents a representation
language in the notation of FOPC whose form facilitates
the design of a semantic-network-like retriever.
I. Introduction
We are engaged ina long-term project to construct a
system that can partake in extended English dialogues
on some reasonably well specified range of topics. A
major part of this effort so far has been the specification
of a knowledge representation. Because of the wide
range of issues that we are trying to capture, which
includes the representation of plans, actions, time, and
individuals' beliefs and intentions, it is crucial to work
within a framework general enough to accommodate
each issue. Thus, we began developing our
representation within the first-order predicate calculus.
So far, this has presented no problems, and we aim to
continue within this framework until some problem
forces us to do otherwise.
Given this framework, we need to be able to build
reasonably efficient systems for use in the project. In
particular, the knowledge representation must be able to
support the natural language understanding task. This
requires that certain forms of inference must be made.
~'~ Within a general theorem-proving framework, however,
those inferences desired would be lost within a wide
range of undesired inferences. Thus we have spent
considerable effort in constructing a specialized
inference component that can support the language
understanding task.
Before such a component could be built, we needed
to identify what inferences were desired. Not
surprisingly, much of the behavior we desire can be
found within existing semantic network systems used for
natural language understanding. Thus the question
"What inferences do we need?" can be answered by
answering the question "What's inasemantic network?"
Ever since Woods's [1975] "What's ina Link" paper,
there has been a growing concern for formalization in
the study of knowledge representation. Several
arguments have been made that frame representation
languages and semantic-network languages are syntactic
variants of the f~st-order predicate calculus (FOPC).
The typical argument (e.g., [Hayes, 1979; Nilsson, 1980;
Charniak, 1981a]) proceeds by showing how any given
frame or network representation can be mapped to a
logically isomorphic (i.e., logically equivalent when the
mapping between the two notations is accounted for)
FOPC representation. We emphasize the term "logically
isomorphic" because these arguments have primarily
dealt with the content (semantics) of the representations
rather than their forms (syntax). Though these
arguments are valid and scientifically important, they do
not answer our question.
Semantic networks not only represent information
but facilitate the retrieval of relevant facts. For instance,
all the facts about the object JOHN are stored with a
pointer directly to one node representing JOHN (e.g.,
see the papers in [Findler, 1979]). Another example
concerns the inheritance of properties. Given a fact such
as "All canaries are yellow," most network systems
would automatically conclude that "Tweety is yellow,"
given that Tweety is a canary. This is typically
implemented within the network matcher or retriever.
We have demonstrated elsewhere [Frisch and Allen,
1982] the utility of viewing a knowledge retriever as a
specialized inference engine (theorem prover). A
specialized inference engine is tailored to treat certain
predicate, function, and constant symbols differently
than others. This is done by building into the inference
engine certain true sentences involving these symbols
19
and the control needed to handle with these sentences.
The inference engine must also be able to recognize
when it is able to use its specialized machinery. That is,
its specialized knowledge must be coupled to the
form
of
the situations that it can deal with.
For illustration, consider an instance of the
ubiquitous type hierarchies of semantic networks:
FORDS
I subtype
MUSTANGS
l type
OLD-BLACK
By mapping the types
AUTOS
and
MUSTANGS
to be
predicates which are true only of automobiles and
mustangs respectively, the following two FOPC
sentences are logically isomorphic to the network:
(1.1) V x MUSTANGS(x) ) FORDS(x)
(1.2) MUSTANGS(OLD-BLACK1)
However, these two sentences have not captured the
form of the network, and furthermore, not doing so is
problematic to the design of a retriever. The subtype and
type links have been built into the network language
because the network retriever has been built to handle
them specially. That is, the retriever does not view a
subtype link as an arbitrary implication such as (1.1) and
it does not view a type link as an arbitrary atomic
sentence such as (1.2).
In our representation language we capture the form
as wetl as the content of the network. By introducing
two predicates,
TYPE
and
SUBTYPE,
we capture the
meaning of the type and subtype links.
TYPE(~O
is true
iff the individual i is a member of the type (set of
objects) t, and
SUBTYPE(tl, t 2) is
true iff the type
t I
is
a subtype (subset) of the type
t 2.
Thus, in our language,
the following two sentences would be used to represent
what was intended by the network:
(2.1) SUBTYPE(FORDS,MUSTANGS)
(2.2) TYPE(OLD-BLACK1,FORDS)
It is now easy to build a retriever that recognizes
subtype and type assertions by matching predicate
names. Contrast this to the case where the representation
language used (1.1) and (1.2) and the retriever would
have to recognize these as sentences to be handled ina
special manner.
But what must the retriever know about the
SUBTYPE and TYPE predicates in order that it can
reason (make inferences) with them? There are two
assertions, (A.1) and (A.2), such that {(1.1),(1.2)} is
logically isomorphic to {(2.1),(2.2),(A.1),(A.2)}. (Note:
throughout this paper, axioms that define the retriever's
capabilities will be referred to as
built-in axioms
and
specially labeled A.1, A.2, etc.)
(A.1) v tl,t2,t 3 SUBTYPE(tl,t2) A SUBTYPE(t2,t3)
, SUBTYPE(tl,t3)
(SUBTYPE is
transitive.)
(A.2) v O,tl,t 2 TYPE(o,tl) A SUBTYPE(tl,t2)
TYPE(o,t2)
(Every member of a given type is a member of
its supertypes.)
The retriever will also need to know how to control
inferences with these axioms, but this issue is considered
only briefly in this paper.
The design of a semantic-network language often
continues by introducing new kinds of nodes and links
into the language. This process may terminate with a
fixed set of node and link types that are the knowledge-
structuring primitives out of which all representations
are built. Others have referred to these knowledge-
structuring primitives as epistemological primitives
[Brachman, 1979], structural relations [Shapiro, 1979],
and system relations [Shapiro, 1971]. If a fLxed set of
knowledge-structuring primitives is used in the language,
then a retriever can be built that knows how to deal with
all of them.
The design of our representation language very
much mimics this approach. Our knowledge-structuring
primitives include a fixed set of predicate names and
terms denoting three kinds of elements in the domain.
We give meaning to these primitives by writing domain-
independent axioms involving them. Thus far in this
paper we have introduced two predicates
(TYPE
and
SUBTYPE'),
two kinds of elements (individuals and
types), and two axioms ((A.1) and (A.2)). We shall name
types in uppercase and individuals in uppercase letters
followed by at least one digit.
Considering the above analysis, a retrieval now is
viewed as an attempt to prove some queried fact
logically follows from the
base facts
(e.g., (2.1), (2.2)) and
the built-in axioms (such as A.1 and A.2). For the
purposes of this paper, we can consider aa~ t~ase facts to
be atomic formulae (i.e., they contain no logical
operators except negation). While compound formulae
such as disjunctions can be represented, they are of little
use to the semantic network retrieval facility, and so will
20
not be considered in this paper. We have implemented a
retriever along these lines and it is currently being used
in the Rochester Dialogue System [Allen, 1982].
2. The Basic Representation: Objects, Events, and
Relations
An important property of a natural language system
is that it often has only partial information about the
individuals (objects, events, and relations) that are talked
about. Unless one assumes that the original linguistic
analysis can resolve all these uncertainties and
ambiguities, one needs to be able to represent partial
knowledge. Furthermore, the things talked about do not
necessarily correspond to the world: objects are
described that don't exist, and events are described that
do not occur.
In order to be able to capture such issues we will
need to include in the domain all conceivable
individuals (cf. all conceivable concepts [Brachman,
1979]). We will then need predicates that describe how
these concepts correspond to reality. The class, of
individuals in the world is subcategorized into three
major classes: objects, events, and relations. We consider
each in turn.
2.1 Objects
Objects include all conceivable physical objects as
well as abstract objects such as ideas, numbers, etc. The
most important knowledge about any object is its type.
Mechanisms for capturing this were outlined above.
Properties of objects are inherited from statements
involving universal quantification over the members of a
type. The fact that a physical object, o, actually exists in
the world will be asserted as
1S-REAL(o).
2.2 Events
The problems inherent in representing events and
actions are well described by Davidson [1967]. He
proposes introducing events as elements in the domain
and introducing predicates that modify an event
description by adding a role (e.g., agent, object) or by
modifying the manner in which the event occurred. The
same approach has been used in virtually all semantic
network- and frame-based systems [Charniak, 1981b],
most of which use a case grammar [Fillmore, 1968] to
influence the choice of role names. This approach also
enables quantification over events and their components
such as in the sentence, "For each event, the actor of the
event causes that event." Thus, rather than representing
the assertion that the ball fell by a sentence such as
(try-l) FALL(BALL1),
the more appropriate form is
(try-2) 3 e TYPE(e,FALL-EVENTS) A
OBJECT-ROLE(e,BALL1).
This formalism, however, does not allow us to make
assertions about roles in general, or to assert that an
object plays some role in an event. For example, there is
no way to express "Role fillers are unique" or "There is
an event in which John played a role." Because we do
not restrict ourselves to binary relations, we can
generalize our representation by introducing the
predicate
ROLE
and making rolenames into individuals
in the domain.
ROLE(o, r, v)
asserts that individual o has
a role named r that is filled with individual v. To
distinguish rolenames from types and individuals, we
shall use italics for rolenames.
Finally, so that we can discuss events that did not
occur (as opposed to saying that such an event doesn't
exis0, we need to add the predicate
OCCUR.
OCCUR(e)
asserts that event e actually occurred. Thus,
finally, the assertion that the ball fell is expressed as
(3)
3 e TYPE(e,FALL-EVENTS) A
ROLE(e,OBJECT, BALL1) A
OCCUR(e).
Roles are associated with an event type by asserting
that every individual of that type has the desired role.
To assert that every event has an
OBJECT
role, we state
(4)
v e 3 r TYPE(e, EVENTS)
ROLE(e, OBJECT, r).
Given this formulation, we could now represent that
"some event occurred involving John" by
(5)
a e, rolename
TYPE(e,EVENTS) A
ROLE(e, rolename, JOHN1) A
OCCUR(e)
By querying fact (5) in our retriever, we can find all
events involving John.
One of the most important aspects of roles is that
they are functional, e.g., each event has exactly one
object role, etc. Since this is important in designing an
efficient retriever, it is introduced as a built-in axiom:
(A.3) v r,o,vl,v2 ROLE(o,r, vl) A ROLE(o,r,v2)
, (vl = v2).
2.3 Relations
The final major type that needs discussing is the
class of relations. The same problems that arise in
representing events arise in representing relations, l:or
21
instance, often the analysis of a simple noun-noun
phrase such as "the book cook" initially may be only
understood to the extent that some relationship holds
between "book" and "cook." If we" want to represent
this, we need to be able to partially describe relations.
This problem is addressed insemantic networks by
describing relations along the same lines as events.
For example, rather than expressing "John is 10" as
(6) AGE-OF(JOHN1,10)
we use the
TYPE
and
ROLE
predicates introduced
above to get
(7) 3 p TYPE(p,AGE-RELATIONS) A
ROLE(p, OBJECT, JOHN1) A
ROLE(p, VALUE,10).
This, of course, mirrors asemantic network such as
AGE-RE~.ATIONS
I type
P1
objects ~,.~alue
JOHN1 10
As with events, describing a relation should not entail
that the relation holds. If this were the case, it would be
difficult to represent non-atomic sentences such as a
disjunction, since in describing one of the disjuncts, we
would be asserting that the disjunct holds. We assert that
a relation, r, is true with
HOLDS(r).
Thus the assertion
that "John is 10" would involve (7) conjoined with
HOLDS(p),
i.e.,
(8) ] p TYPE(p,AGE-RELATIONS) A
ROLE(p, OBJECT, JOHN1) A
ROLE(p, VALUE, IO) ^
HOLDS(p)
The assertion "John is not 10" is not the negation of (8),
but is (7) conjoined with
-HOLDS(p),
i.e.,
(9) ] p TYPE(p,AGE-RELATIONS) A
ROLE(p, OBJECT;JOHN1) A
ROLF(p,
VALUE, IO) A
-HOLDS(p).
We could also handle negation by introducing the
type NO'I'-REIATIONS, which takes one rd. ~,.,,, is
filled by another relation. To assert the above, we woutd
construct an individual N1, of type NOT-RELATIONS,
with its role filled with p, and assert that N1 holds. We
see no advantage to this approach, however, since
negation "moves through" the HOLDS predicate. In
other words, the relation "not p" holding is equivalent to
the relation "p" not holding. Disjunction and
conjunction are treated ina similar manner.
3. Making Types Work
for You
The system described so far, though simple, is close
to providing us with one of the most characteristic
inferences made by semantic networks, namely
inheritance. For example, we might have the following
sort of information in our network:
(10) SUBTYPE(MAMMALS,ANIMALS)
(11) S UBTYPE(2-LEGGED-ANIMALS,ANIMALS)
(12) SUBTYPE(PERSONS,MAMMALS)
(13) SUBTYPE(PERSONS,2-LEGGED-ANIMALS)
(14) SUBTYPE(DOGS,MAMMALS)
(15) TYPE(GEORGE1,PERSONS)
In a notation like in [Hendrix, 1979], these facts would
be represented as:
ANIMALS
2-LE MAMMALS
PERSONS DOGS
T
GEORGE1
In addition, let us assume we know that all instances of
2-LEGGED-ANIMALS have two legs and that all
instances of MAMMALS are warm-blooded:
(16)
v x TYPE(x,2-LEGGF_.D-ANIMALS)
HAS-2-LEGS(x)
(17)
v y TYPE(y,MAMMALS) .
-~ WARM-BLOODED(y)
These would be captured in the Hendrix formalism
using his delineation mechanism.
Note that relations such as "WARM-BLOODED"
and "HAS-2-LEGS" should themselves be described as
relations with roles, but that is not necessary for this
example. Given these facts, and axioms (A.1) to (A.3),
we can prove that "George has two legs" by using axiom
(A.2) on (13) and (15) to conclude
(18) TYPE(GEORGE1,2-LEGGED-ANIMALS)
22
and then using (18) with (16) to conclude
(19) HAS-2-LEGS(GEORGE1).
In order to build a retriever that can perform these
inferences automatically, we must be able to distinguish
facts like (16) and (17) from arbitrary facts involving
implications, for we cannot allow arbitrary chaining and
retain efficiency. This could be done by checking for
implications where the antecedent is composed entirely
of type restrictions, but this is difficult to specify. The
route we take follows the same technique described
above when we introduced the TYPE and SUBTYPE
predicates. We introduce new notation into the language
that explicitly captures these cases. The new form is
simply a version of the typed FOPC, where variables
may be restricted by the type they range over. Thus, (16)
and (17) become
(20) v x:2-LEGGED-ANIMAI.S HAS-2-LEGS(x)
(21) V y:MAMMALS WARM-BLOODED(y),
The retriever now can be implemented as a typed
theorem prover that operates only on atomic base facts
(now including (20) and (21)) and axioms (A.1) to (A.3).
We now can deduce that GEORGE1 has two legs
and that he is warm-blooded. Note that objects can be of
many different types as well as types being subtypes of
different types. Thus, we could have done the above
without the type PERSONS, by making GEORGE1 of
type 2-LEGGED-ANIMALS and MAMMALS.
4. Making Roles Work for You
In the previous section we saw how properties could
be inherited. This inheritance applies to role assertions
as well. For example, given a type EVILNTS that has an
OBJECT
role. i.e.,
(22) SUBTYPE(EVENTS,INDIVIDUALS)
(23) v x:EVENTS
3 y:PHYS-OBJS
ROLE(x, OBJECT, y).
Then if ACTIONS are a subtype of events, i.e.,
(24) SUBTYPE(ACTIONS,EVENTS),
it follows from (A.2), (23), and (24) that for every action
there is something that fills its
OBJECT
role, i.e.,
(25) v x:ACTIONS
3 y:PHYS-OBJS
ROLE(x,OBJECT;y).
Note that the definition of the type ACTIONS could
further specify the type of the values of its
OMI".CT
role, but it could not contradict fact (25). Thus
(26)
V x:ACTIONS
3 y:PERSONS
ROLE(x, OBJECT, y),
further restricts the value of the
OBJECT
role for all
individuals of type ACTIONS to be .of type PERSONS.
Another common technique used insemantic
network systems is to introduce more specific types of a
given type by specifying one (or more) of the role
values. For instance, one might introduce a subtype of
ACTION called ACTION-BY-JACK, i.e.,
(27)
(28)
SUBTYPE(ACTION-BY-JACK,ACTIONS)
¥ abj:ACTION-BY-JACK
ROLE(abj,ACTOR,JACK).
Then we could encode the general fact that all actions by
Jack are violent by something like
(29) v abj:ACTION-BY-JACK
VIOLENT(abj).
This is possible in our logic, but there is a more flexible
and convenient way of capturing such information. Fact
(29), given (27) and (28),
is equivalent to
(30) v a:ACTIONS
(ROLE a ACTOR JACK)
• , VIOLENT(a).
If we can put this into a form that is recognizable to the
retriever, then we could assert such facts directly without
having to introduce arbitrary new types.
The extension we make this time is from what we
called a type logic to a role logic. This allows quantified
variables to be restricted by role values as well as type.
Thus, in this new notation, (30) would be expressed as
(31) v a:ACH'IONS [ACTOR JACK]
VIOLENT(a).
In general, a formula of the form
v a:T [R1V1] [RnVn] Pa
is equivalent to
v a (TYPE(a,T) A
ROLE(a,R1,V1) AA ROLE(a,Rn,Vn))
• -* Pa.
23
Correspondingly, an existentially cluantitied formula
such as
3 a:T [R1V1] [RnVn] Pa
is equivalent to
3 a TYPE(a,T) A
ROLE(a, R1,V1) A ^ ROLE(a,Rn,V n) ^
Pa.
The retriever recognizes these new forms and fully
reasons about the role restrictions. It is important to
remember that each of these notation changes is an
extension onto the original simple language. Everything
that could be stated previously can still be stated. The
new notation, besides often being more concise and
convenient, is necessary only if the semantic network
retrieval facilities are desired.
Note also that we can now define the inverse of (28),
and state that all actions with actor JACK are necessarily
of type ACTION-BY-JACK. This can be expressed as
(32) v a:ACTIONS [ACTOR JACK]
TYPE(a, ACTION-BY-JACK).
5. Equality
One Of the crucial facilities needed by natural
language systems is the ability to reason about whether
individuals are equal. This issue is often finessed in
semantic networks by assuming that each node
represents a different individual, or that every type in
the type hierarchy is disjoint. This assumption has been
called E-saturation by [Reiter, 1980]. A natural language
understanding system using such a representation must
decide on the referent of each description as the
meaning representation is constructed, since if it creates
a new individual as the referent, that individual will then
be distinct from all previously known individuals. Since
in actual discourse the referent of a description is not
always recognized until a few sentences later, this
approach lacks generality.
One approach to this problem is to introduce full
reasoning about equality into the representation, but this
rapidly produces a combinatorially, prohibitive search
space. Thus other more specialized techniques are
desired. We shall consider mechanisms for proving
inequality f'trst, and then methods for proving equality.
Hendrix [1979] introduced some mechanisms that
enable inequality to be proven. In his system, mere are
two forms of subtype links, and two forms of instance
links. This can be viewed in our system as follows: the
SUBTYPE and TYPE predicates discussed above make
no commitment regarding equality. However, a new
relation, DSUBTYPE(tl,t2) , asserts that t 1 is a
SUBTYPE of t 2, and also that the elements of t 1 are
distinct from all other elements of other DSUBTYPES
oft 2. This is captured by the axioms
(A.4)
v t, tl,t2,il,i2
(DSUBTYPE(tl,t) A DSUBTYPE(t2,t) A
TYPE(il,tl) A TYPE(i2,t 2) A
~IDENTICAL(tl,t2))
,
(i 1 *
i 2)
(A.5) v tl,t DSUBTYPE(tl,t) , SUBTYPE(tl,t)
We cannot express (A.4) in the current logic because the
predicate IDFA',ITICAL operates on the syntactic form of
its arguments rather than their referents. Two terms are
IDENTICAL only if they are lexicaUy the same. To do
this formally, we have to be able to refer to the syntactic
form of terms. This can be done by introducing
quotation into the logic along the lines of [Perlis, 1981],
but is not important for the point of this paper.
A similar trick is done with elements of a single type.
The predicate DTYPE(i,t) asserts that i is an instance of
type t, and also is distinct from any other instances of t
where the DTYPE holds. Thus we need
(A.6)
v il,i2,t (DTYPE(il,t) A DTYPE(i2,t) A
~ IDENTICAL(il,i2) )
• , (i 1 * i 2)
(A.7) vi, t DTYPE(i,t) , TYPE(i,t)
Another extremely useful categorization of objects is
the partitioning of a type into a set of subtypes, i.e., each
element of the type is a member of exactly one subtype.
This can be defined ina similar manner as above.
Turning to methods for proving equality, [Tarjan,
1975] describes an efficient method for computing
relations that form an equivalence class. This is adapted
to support full equality reasoning on ground terms. Of
course it cannot effectively handle conditional assertions
of equality, but it covers many of the typical cases.
Another technique for proving equality exploits
knowledge about types. Many types are such that their
instances are completely defined by their roles. For such
a type T, if two instances I1 and 12 of T agree on all
their respective rc!~ then they are equal. If I1 and I2
have a role where their values are not equal, then I I and
I2 are not equal. If we finally add the assumption that
every instance of T can be characterized by its set of role
values, then we can enumerate the instances of type T
using a function (say t) that has an argument for each
role value.
24
For example, consider the type AGE-RELS of age
properties, which takes two roles, an OBJECT and a
VALUE. Thus, the property P1 that captures the
assertion "John is 10" would be described as follows:
(33) TYPE(P1,AGE-RELS) A
ROLE(PI,OBJECT, JOHN1) A
ROLE(P1, VALUE, IO).
The type AGE-RELS satisfies the above properties,
so any individual of type AGE-RELS with OBJECT
role JOHN1 and VALUE role 10 is equal to P1. The
retriever encodes such knowledge ina preprocessing
stage that assigns each individual of type AGE-RELS to
a canonical name. The canonical name for P1 would
simply be "age-rels(JOHNl,10)".
Once a representation has equality, it can capture
some of the distinctions made by perspectives in KRL.
The same object viewed from two different perspectives
is captured by two nodes, each with its own type, roles,
and relations, that are asserted to be equal.
Note that one cannot expect more sophisticated
reasoning about equality than the above from the
retriever itself. Identifying two objects as equal is
typically not a logical inference. Rather, it is a plausible
inference by some specialized program such as the
reference component of a natural language system which
has to identify noun phrases. While the facts represented
here would assist such a component in identifying
possible referencts for a noun phrase given its
description, it is unlikely that they would logically imply
what the referent is.
6. Associations and Partitions
Semantic networks are useful because they structure
information so that it is easy to retrieve relevant facts, or
facts about certain objects. Objects are represented only
once in the network, and thus there is one place where
one can find all relations involving that object (by
following back over incoming ROLE arcs). While we
need to be able to capture such an ability in our system,
we should note that this is often not a very useful ability,
for much of one's knowledge about an object will ,lot be
attached to that object but will be acquired from the
inheritance hierarchy. Ina spreading activation type of
framework, a considerable amount of irrelevant network
will be searched before some fact high up in the type
hierarchy is found. In addition, it is very seldom that
one wants to be able to access all facts involving an
object; it is much more likely that a subset of relations is
relevant.
If desired, such associative links between objects can
be simulated in our system. One could find all properties
of an object ol (including those by inheritance) by
retrieving all bindings of x in the query
3x,r ROLE(x,r,ol).
The ease of access provided by the links inasemantic
network is effectively simulated simply by using a
hashing scheme on the structure of all ROLE predicates.
While the ability to hash on structures to find facts is
crucial to an efficient implementation, the details are not
central to our point here.
Another important form of indexing is found in
Hendrix where his partition mechanism is used to
provide a focus of attention for inference processes
[Grosz, 1977]. This is just one of the uses of partitions.
Another, which we did not need, provided a facility for
scoping facts within logical operators, similar to the use
of parentheses in FOPC. Such a focus mechanism
appears in our system as an extra argument on the main
predicates (e.g., HOLDS, OCCURS, etc.).
Since contexts are introduced as a new class of
objects in the language, we can quantify over them and
otherwise talk about them. In particular, we can organize
contexts into a lattice-like structure (corresponding to
Hendrix's vistas for partitions) by introducing a
transitive relation SUBCONTEXT.
(A.8) v
c,cl,c2 SUBCONTEXT(c,cl) A
SUBCONTEXT(cl,c2)
SUBCONTEXT(c,c2)
To relate contexts to the HOLDS predicate, a
proposition p holds ina context c only if it is known to
hold in c explicitly, or it holds ina super context of c.
(A.9)
v p,t,c,c' SUBCONTEXT(c,c,)A
HOt.DS(p,c')
, HOLDS(p,c),
As with the SUBTYPE relation, this axiom would defy
an efficient implementation if the contexts were not
organized ina finite lattice structure. Of course, we need
axioms similar to (A,9) for the OCCURS and IS-RF_.AL
predicates.
7. Discussion
We have argued that the appropriate way to design
knowledge representations is to identify those inferences
that one wishes to facilitate. Once these are identified,
one can then design a specialized limited inference
mechanism that can operate on a data base of first order
25
facts.
In this fashion, one obtains a highly expressive
representation language (namely FOPC), as well as a
well-defined and extendable retriever.
We have demonstrated this approach by outlining a
portion of the representation used in ARGOT, the
Rochester Dialogue System [Allen, 1982]. We are
currently extending the context mechanism to handle
time, belief contexts (based on a syntactic theory of
belief [Haas, 1982]), simple hypothetical reasoning, and a
representation of plans. Because the matcher is defined
by a set of axioms, it is relatively simple to add new
axioms that handle new features.
For example, we are currently incorporating a model
of temporal knowledge based on time intervals [Allen,
1981a]. This is done by allowing any object, event, or
relation to be qualified by a time interval as follows: for
any untimed concept x, and any time interval t, there is
a timed concept consisting of x viewed during t which is
expressed by the term
(t-concept x t).
This concept is of type (TIMED Tx), where Tx is the
type of x. Thus we require a type hierarchy of timed
concepts that mirrors the hierarchy of untimed concepts.
Once this is done, we need to introduce new built-in
axioms that extend the retriever. For instance, we define
a predicate,
DURING(a,b),
that is true only if interval a is wholly contained in
interval b. Now, if we want the retriever to automatically
infer that if relation R holds during an interval t, then it
holds in all subintervals of t, we need the following
built-in axioms. First, DURING is transitive:
(A.10) V a,b,c DURING(a,b) A DURING(b,c)
, DURING(a,c)
Second, if P holds in interval t, it holds in all
subintervals of t.
(A.11) v p,t,t',c HOLDS(t-concept(p,t),c) A
DURING(t' ,t)
, HOLDS(t-concept(p,t'),c).
Thus we have extended our representation to handle
simple timed concepts with only a minimal amount of
analysis.
Unfortunately, we have not had the space to
describe how to take the specification of the retriever
(namely axioms (A.1) - (A.11)) and build an actual
inference program out of it. A technique for building
such a limited inference mechanism by moving to a
meta-logic is described in [Frisch and Allen, 1982].
One of the more interesting consequences of this
approach is that it has led to identifying various
difference modes of retrieval that are necessary to
support a natural language comprehension task, We
have considered so far only one mode of retrieval, which
we call
provability mode.
In this mode, the query must
be shown to logically follow from the built-in axioms
and the facts in the knowledge base. While this is the
primary mode of interaction, others are also important.
In
consistency mode, the
query is checked to see if it
is logically consistent with the facts in the knowledge
base with respect to the limited inference mechanism.
While consistency in general is undecidable, with respect
to the limited inference mechanism it is computationally
feasible. Note that, since the retriever is defined by a set
of axioms rather than a program, consistency mode is
easy to define.
Another important mode is
compatibility mode,
which is very useful for determining the referents of
description. A query in compatibility mode succeeds if
there is a set of equality and inequality assertions that
can be assumed so that the query would succeed in
provability mode. For instance, suppose someone refers
to an event in which John hit someone with a hat. We
would like to retrieve possible events that could be equal
to this. Retrievals in compatibility mode are inherently
expensive and so must be controlled using a context
mechanism such as in [Grosz, 1977]. We are currently
attempting to formalize this mode using Reiter's non-
monotonic logic for default reasoning.
We have implemented a version of this system in
HORNE [Allen and Frisch, 1981], a LISP embedded
logic programming language. In conjunction with this
representation is a language which provides many
abbreviations and facilities for system users. For
instance, users can specify what context and times they
are working with respect to, and then omit this
information from their interactions with the system.
Also, using the abbreviation conventions, the user can
describe a relation and events without explicitly asserting
the TYPE and ROLE assertions. Currently the system
provides the inheritance hierarchy, simple equality
reasoning, contexts, and temporal reasoning with the
DURING hierarchy.
26
Acknowledgments
This research was supported in part by the National
Science Foundation under Grant IST-80-12418, and in
part by the Office of Naval Research under Grant
N00014-80-C-0197.
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27
. introducing the
predicate
ROLE
and making rolenames into individuals
in the domain.
ROLE(o, r, v)
asserts that individual o has
a role named r that is. often has only partial information about the
individuals (objects, events, and relations) that are talked
about. Unless one assumes that the original linguistic